Predicting the Performance of Teams of Bounded Rational Decision-makers Using a Markov Chain Model

Abstract

In practice, when faced with a complex optimization problem, teams of human decision-makers often separate it into subproblems and then solve each subproblem instead of tackling the complete problem. It would be useful to know the conditions in which separating the problem is the superior approach and how the subproblems should be assigned to members of the teams. This paper describes a mathematical model of a search that represents a bounded rational decision-maker (“agent”) solving a generic optimization problem. The agent’s search can be modeled as a discrete-time Markov chain, which allows one to calculate the probability distribution of the value of the solution that the agent will find. We compared the distributions generated by the model to the distribution of results from searches of solutions to traveling salesman problems. Using this model, we evaluated the performance of two- and three-agent teams who used different solution approaches to solve generic optimization problems. In the “all-at-once” approach, the agents collaborate to search the entire set of solutions in a sequential manner: the next agent begins where the previous agent stopped. In the “separation” approach, the agents separate the problem into two subproblems: (1) find the best set of solutions, and (2) find the best solution in that set. The results show that teams found better solutions using separation when high-value solutions are less likely. Using the all-at-once approach yielded better results when the values were uniformly distributed. The optimal assignment of subproblems to teams also depended upon the distribution of values in the solution space.